Interest in automatic action and gesture recognition has grown considerably in the last few years. This is due in part to the large number of application domains for this type of technology. As in many other computer vision areas, deep learning based methods have quickly become a reference methodology for obtaining state-of-the-art performance in both tasks. This chapter is a survey of current deep learning based methodologies for action and gesture recognition in sequences of images. The survey reviews both fundamental and cutting edge methodologies reported in the last few years. We introduce a taxonomy that summarizes important aspects of deep learning for approaching both tasks. Details of the proposed architectures, fusion strategies, main datasets, and competitions are reviewed. Also, we summarize and discuss the main works proposed so far with particular interest on how they treat the temporal dimension of data, their highlighting features, and opportunities and challenges for future research. To the best of our knowledge this is the first survey in the topic. We foresee this survey will become a reference in this ever dynamic field of research.